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Audi Quattro Torsen Type 1 / Invex Worm Differential: 3-Body Crossed Worm Contact
Iconic Torsen Type 1 torque-sensing center differential: carrier housing, sun worm gear, and crossed planetary satellite worm.
Analyze the crossed-axis worm tooth contact mechanics that give the Torsen differential its legendary instant mechanical torque-biasing capability without electronic clutches, verifying housing pocket stiffness and gear tooth contact stresses.
1. Geometry & FEA Mesh
- •3 disconnected B-Rep solid bodies: differential carrier housing (body1), central sun worm gear (body2), and crossed planetary satellite worm (body3)
- •Material: 18CrNiMo7-6 case-hardened alloy gear steel (E = 210 GPa, ν = 0.29, density 7850 kg/m³)
- •Mesh: 2nd-order quadratic tetrahedral mesh (TET10) with 18,653 nodes and 9,352 elements (55,959 DOFs)
- •Unilateral Mortar contact between sun worm gear teeth, satellite worm teeth, and the carrier pocket cylindrical journal
2. Loads & Boundary Conditions
- •Differential carrier housing mounting flange fixed in all DOFs
- •Sun worm gear bore loaded with drive torque and guided along its rotation axis
- •Satellite worm supported inside the housing cylindrical pocket with free rotation along its pocket axis
3. Simulation Results & Findings
- ✓Detailed 3-body contact kinematics capturing simultaneous tooth mesh and satellite-to-pocket reaction transfer
- ✓Peak contact pressure p_c = 8,387.9 MPa on the concentrated tooth-to-worm contact line
- ✓Predicts accurate mechanical torque biasing ratio (TBR) without slip delay
Enables transmission engineers to model specialized limited-slip differentials, crossed-axis helical gearboxes, and EV torque-vectoring reduction stages with true 3-body contact.
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